Details

Time bar (total: 3.7s)

sample54.0ms

Algorithm
intervals
Results
21.0ms43×body2560valid
9.0ms38×body1280valid
9.0ms56×body640valid
3.0ms31×body320valid
3.0ms74×body80valid
1.0ms14×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.0b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.0b
(- 1.0 (cos x))
14.7b
(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 42
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
7.0ms
(/ (- 1.0 (cos x)) (* x x))

series67.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(- 1.0 (cos x))
48.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify67.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune139.0ms

Filtered
48 candidates to 34 candidates (70.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New381048
Fresh000
Picked101
Done000
Total391049

Merged error: 0.0b

Counts
49 → 10

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- 1.0 (cos x)) x) x)
0.1b
(/ (- 1.0 (cos x)) x)
1.0b
(- 1.0 (cos x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
103×add-sqr-sqrt *-un-lft-identity
69×add-cube-cbrt
24×associate-/l*
17×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg diff-log
Counts
3 → 147
Calls
3 calls:
9.0ms
(/ (/ (- 1.0 (cos x)) x) x)
6.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series137.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(/ (/ (- 1.0 (cos x)) x) x)
67.0ms
(/ (- 1.0 (cos x)) x)
22.0ms
(- 1.0 (cos x))

simplify51.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
05311270
118991197
250011186

prune246.0ms

Filtered
156 candidates to 102 candidates (65.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1524156
Fresh369
Picked101
Done000
Total15610166

Merged error: 0.0b

Counts
166 → 10

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b
(/ (cos x) x)
1.2b
(- (/ 1.0 x) (/ (cos x) x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
98×add-sqr-sqrt
95×times-frac
78×*-un-lft-identity
38×add-cube-cbrt
20×distribute-lft-out-- difference-of-squares
15×associate-/l*
12×div-inv
7×add-exp-log add-cbrt-cube
6×associate-/r*
5×distribute-rgt-out-- add-log-exp
4×associate-/l/
3×pow1
2×cbrt-undiv flip3-- frac-2neg div-exp clear-num frac-sub flip-- sub-div
1×sub-neg diff-log div-sub
Counts
3 → 118
Calls
3 calls:
16.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
4.0ms
(/ (cos x) x)
16.0ms
(- (/ 1.0 x) (/ (cos x) x))

series196.0ms

Counts
3 → 9
Calls
3 calls:
103.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
30.0ms
(/ (cos x) x)
63.0ms
(- (/ 1.0 x) (/ (cos x) x))

simplify51.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04631015
11518940
25002936

prune232.0ms

Filtered
127 candidates to 100 candidates (78.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1252127
Fresh369
Picked101
Done000
Total1298137

Merged error: 0.0b

Counts
137 → 8

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (- (/ 1.0 x) (/ (cos x) x)) (/ 1 x))
0.1b
(/ (cos x) x)
1.2b
(- (/ 1.0 x) (/ (cos x) x))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
40×*-un-lft-identity times-frac
23×add-cube-cbrt
14×add-exp-log
13×associate-*r*
12×associate-*l*
10×add-cbrt-cube
8×distribute-lft-out-- difference-of-squares
6×div-inv
5×pow1 add-log-exp
4×frac-times associate-*l/ prod-exp
3×flip3-- div-exp associate-/r* frac-sub flip-- associate-/l* sub-div unswap-sqr
2×cbrt-undiv distribute-rgt-out-- cbrt-unprod
1×sub-neg rec-exp frac-2neg diff-log 1-exp associate-*r/ pow-prod-down clear-num un-div-inv *-commutative
Counts
3 → 103
Calls
3 calls:
20.0ms
(* (- (/ 1.0 x) (/ (cos x) x)) (/ 1 x))
4.0ms
(/ (cos x) x)
13.0ms
(- (/ 1.0 x) (/ (cos x) x))

series254.0ms

Counts
3 → 9
Calls
3 calls:
104.0ms
(* (- (/ 1.0 x) (/ (cos x) x)) (/ 1 x))
51.0ms
(/ (cos x) x)
98.0ms
(- (/ 1.0 x) (/ (cos x) x))

simplify56.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0441753
12022677
25001659

prune180.0ms

Filtered
112 candidates to 87 candidates (77.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1120112
Fresh077
Picked011
Done000
Total1128120

Merged error: 0.0b

Counts
120 → 8

regimes71.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.7b

bsearch68.0ms

Steps
ItersRangePoint
9
2.1876360655290875e-05
7233.4722653017725
0.03566577089523101
8
-1.5124741638829355
-8.4755032599275e-05
-0.0388630285242168

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03512
13512

end0.0ms

sample1.7s

Algorithm
intervals
Results
765.0ms1575×body2560valid
288.0ms1199×body1280valid
251.0ms1511×body640valid
105.0ms922×body320valid
90.0ms2320×body80valid
37.0ms473×body160valid

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